Set-membership Filtering For Genetic Regulatory Networks

With the development of system biology,genetic regulatory networks can represent the expression of genetic information and has been one of the hottest topics in bioinformatics.A class of discrete-time genetic regulatory networks with time delays,parameter uncertainties and noise is considered in this paper.A set-membership filtering method is proposed to estimate the states of the underlying genetic regulatory networks.In this filtering method,it assumes that measurement noises of the process is unknown-but-bounded.Thus,it does not need the knowledge of noise statistics.Moreover,the corresponding problem of set-membership filtering is formulated as finding the set of estimations that belongs to an ellipsoid.The main research work and contributions of this dissertation are summarized as follows:First,in this paper,we make an overview of the main contents of genetic regulatory networks,and analysis of the common model of genetic regulatory networks.It reveals the impact of regulatory processes with the presence of time delays,parameter uncertainties and molecular noise.At the same time,we make an overview of the status of research of set-membership filtering theory,and describes the advantages of set-membership filtering.Then,considering the problems exists in the ideal genetic regulatory networks model,for example,the influences of the following factors are unconsidered:in biological systems,time delay is generated primarily due to the slow processes of transcription,translation and translocation;parameter uncertainties are existed due to the fluctuations in the number of molecules;and the nature of the noise and its value may not be fully known or measurable due to complexity of biological processes.Therefore,a discrete-time genetic regulatory networks with time delays,parameter uncertainties and noise is built to reflect the real state of the genetic regulatory networks.The data missing is a common and important problem in the area of genetic regulatory networks.Based on the built discrete-time genetic regulatory networks with time delays,parameter uncertainties and noise,by using S-procedure,Schur Complement and LMI methods,a set membership filtering method is designed to eliminate the effect of the data missing on the state observation.Finally,a recursive algorithm is developed for computing the set membership filtering.The simulation result shows that the method presented is available and effective.The state constraints is a common and important problem in the area of genetic regulatory networks.A class of discrete-time genetic regulatory networks with time delays,parameter uncertainties and noise is considered.Then,Finsler’s Lemma is employed to project the unconstrained set membership filtering onto the constrained surface.Finally,we consider the state equality constraints of two gene as an example to show the effectiveness and correctness of our theoretical results.Finally,summarizes the contents of this paper,and pointed out the future research of genetic regulatory networks.